Suppose the demand equation facing a firm is Q=1000-5Q, MR=200-0.4Q, and MC=$20.

A. Compute the maximum profit the firm can earn.

B. Suppose the firm is considering a quantity discount. It offers the first 400 units at a price of $120, and further units at a price of $80. How many units will the consumer buy in total?

C. Compute the profit if the quantity discount is implemented.

D. If the firm implemented a two part pricing strategy, what would be the fixed fee, variable fee, total revenue, and the total variable cost?

1. A rapidly growing firm is currently paying a dividend of $90. The dividend growth rate is expected to be 12% for the next 6 years. The dividend growth rate after the first 6 years is expected to be 3% annually. The expected return on the market is 8%, the risk free rate is 3% and the firm’s Beta is 25.
   1. Calculate the estimated price (intrinsic value) for a share of this firm’s stock.
   2. What does this firm’s Beta measure?
   3. Use Goal Seek to determine what the current dividend would need to be to yield an estimated price (intrinsic value) of $95.

32. Gas Prices for Rental Cars The first column of these data represents the prebuy gas price of a rental car, and the second column represents the price charged if the car is returned without refilling the gas tank for a selected car rental company. Draw two boxplots for the data and compare the distributions. (Note: The data were collected several years ago.)

Prebuy cost                     No prebuy cost

$1.55                                $3.80

1.54                                  3.99

1.62                                  3.99

1.65                                  3.85

1.72                                  3.99

1.63                                  3.95

1.65                                  3.94

1.72                                  4.19

1.45                                  3.84

1.52                                  3.94

PEI Real Estate company believes that their average house price in 2020 of $290,000 is higher than the mean price of all houses sold in 2019 of $270,000. Assuming that their estimate was based on the first 40 sales in 2020 and the population standard deviation of $70,000, test this hypothesis at the 95% confidence interval.

1. State the hypotheses based on a one-tailed test.

2. What is the level of significance?

3. Select a test statistic.  

4. Formulate the decision rule. Sketch this on a graph.

5. Calculate the test value.

6. What is the decision?

7. Does your conclusion change if the 90% confidence interval is selected? Explain.

Due to the pandemic of COVID-19 in the U.S., the price of U.S. crude oil contracts for May 2020 delivery has turned negative for the first time in history. For instance, West Texas Intermediate (WTI) crude oil contracts for May fell 301.97 percent to -$36.90 per barrel.
State your understanding of this phenomenon and carefully explain your arguments with economic tools and/or economic intuition, including the aspects of
1.   demand for oil by households;
2.   demand for oil by non-household demanders, such as manufacturers;
3.   market supply of oil;
4.   equilibrium price and quantity.

Using the bond below, calculate your annual holding period yield (on a bond equivalent basis).

• 3.096%
• 5.888%
• 6.192%
• 6.246%
• 6.288%

1. A rapidly growing firm is currently paying a dividend of $2.20. The dividend growth rate is expected to be 9% for the next 8 years. The dividend growth rate after the first 8 years is expected to be 4% annually. The expected return on the market is 7%, the risk free rate is 4% and the firm’s Beta is 0.84.
   1. Calculate the estimated price (intrinsic value) for a share of this firm’s stock.
   2. What does this firm’s Beta measure?
   3. Use Goal Seek to determine what the current dividend would need to be to yield an estimated price (intrinsic value) of $150.

The spot price of a certain asset is S0 = $50400 And the price for a six months maturity future over such underlying asset is F= $53550

a) Compute the risk free rate (continuous compounding).

b) Combine the spot and the future markets so as to replicate debt. Your wealth is $ 50,400,000, show two strategies that:

 Invest purchasing both, the underlying asset and bonds.

 Invest purchasing only the underlying asset and borrowing money.

(Hint: File called “Options & Futures” by Alejandro Balbás will help you).

The price of a stock is currently $39.38. The stock price by the end of the next three-month period is expected to be up by 10 percent or down by 10 percent. The risk-free interest rate is 1.875 percent per annum with continuous compounding. What is the current value of a three-month European call option with strike price of $34.375 using a single-step binomial tree? How will you trade involving one call option to make arbitrage profits if the call option’s current market price is $9.88?

23. What is the value of p?

What are the two values (cash flows) of the call option at maturity from top to bottom of the tree?

24. Cash flows at the top of the tree.

25. Cash flows at the bottom of the tree.

26. What is the current fair value of the call option?

27. What is the value of delta at time 0?

28. Write 1 if your answer is to take a long position in the call option and 0 if it is to take a short position in the call option in an arbitrage trading strategy at time zero.

29. Write the net cash position (if borrowed write with a negative sign) at time zero. Write the two net cash positions from top to bottom at the end of one step (maturity) in your trading strategy:

30.

31.

32. Write the net cash made as of maturity from the arbitrage trading strategy